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Otherwise, we would reach a contradiction by (15) ((16)) that the constant factor in (12) is not best possible.
Otherwise we would reach a contradiction by (16) and (17) that the constant factor in (13) is not best possible.
However, this inequality is not best possible, but also a 'sharp' variant of this inequality is known.
Otherwise, we would reach a contradiction by (27) that the constant factor (K lambda_{1})) in (24) is not best possible.
If the constant factor c r in (14) is not best possible, then there exists a positive number K, with 0 < K < c r, such that (14) is still valid if we replace c r by K.
In the United States, a Crown Vic (Including the extra-long "Commercial" type), Grand Marquis, Town Car (Including the extra-long "L" type) is a choice of many professionals due to its great size, nice though not best possible comfort, and extreme durability and ease of maintenance.
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For example, it may not be obvious whether having six legs is or is not the "best" possible functional solution for all insects.
If the constant factors in (15) and (16) are not the best possible, then we can imply a contradiction that the constant factor in (14) is not the best possible by (17) and (19).
If the constant factor in (3.1) is not the best possible, then it is known from (3.4) that the constant factor in (2.1) is also not the best possible.
If the constant factor in (12) is not the best possible, then by (16), we would reach a contradiction: that the constant factor in (11) is not the best possible.
If the constant factor in (12) is not the best possible, then by (16), we may get a contradiction: that the constant factor in (11) is not the best possible.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com